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Least-Squares Model-Reference Adaptive Control: Extension to Higher Relative Degree Plants
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DOI：10.1109/tac.2026.3674420.png)
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Abstract
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A Lyapunov-based least-squares model-reference adaptive controller was recently developed for plants with relative degree one. The algorithm exhibits a remarkable tracking error transient performance while also ensuring fast parameter convergence. In this article, we generalize this algorithm to the more complex and challenging case of plants with higher relative degree. The key elements for the design procedure are the strictly positive real (SPR) principle and the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">backstepping</i> technique. The idea here is to employ the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">backstepping</i> technique to retrieve the control law from its filtered signal. This solution, however, requires the derivative of the tracking error, which is provided by a first-order passive observer. The SPR principle, so fundamental to the controller design, is also exploited in the observer design. The proposed SPR observer is the key to replicating the analysis performed for the controller. As a result, least-squares update laws can be employed for both.
Keywords:
Backstepping
least-squares (LS) estimate
Lyapunov stability
model-reference adaptive control (MRAC)
passive adaptive observer
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7
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1.3W
Citations:
6.7W
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